In-Plane Movement Catcher View

\documentclass[12pt]{article}

\usepackage[paperwidth=200pt, paperheight=200pt,margin=12pt]{geometry}
\usepackage{color,tikz,ifthen,animate,pgf}

\begin{document}

% This code will simulate a pitch based on the 9-parameter PITCHf/x model, including the pitch plane and projections for PITCHf/x movement without (red) and with (blue dashed) accounted for.

% Written by Matthew Mata, January 2017.

\thispagestyle{empty}

% Set the counter
\newcounter{m}
\setcounter{m}{0}

% Set the PITCHf/x parameters
\pgfmathsetmacro{\xo}{1.254}
\pgfmathsetmacro{\yo}{50.0}
\pgfmathsetmacro{\zo}{6.101}
\pgfmathsetmacro{\vxo}{-1.23}
\pgfmathsetmacro{\vyo}{-137.906}
\pgfmathsetmacro{\vzo}{-9.567}
\pgfmathsetmacro{\ax}{0.155}
\pgfmathsetmacro{\ay}{35.877}
\pgfmathsetmacro{\az}{1.229}

% Set gravity
\pgfmathsetmacro{\g}{-32.174}

% Set the binormal vector
\pgfmathsetmacro{\Bx}{\vyo*\az - \vzo*\ay}
\pgfmathsetmacro{\By}{\vzo*\ax - \vxo*\az}
\pgfmathsetmacro{\Bz}{\vxo*\ay - \vyo*\ax}
\pgfmathsetmacro{\Bnorm}{100*sqrt((0.01*\Bx)*(0.01*\Bx) + (0.01*\By)*(0.01*\By) + (0.01*\Bz)*(0.01*\Bz))}
\pgfmathsetmacro{\Bx}{\Bx/\Bnorm}
\pgfmathsetmacro{\By}{\By/\Bnorm}
\pgfmathsetmacro{\Bz}{\Bz/\Bnorm}

% Find the fixed B-coordinate
\pgfmathsetmacro{\Bfixed}{\Bx*\xo + \By*\yo + \Bz*\zo}

% Set the vector in the direction of home plate, u
\pgfmathsetmacro{\Ux}{(\Bx/abs(\Bx))*(-\By)/sqrt(\Bx*\Bx + \By*\By)}
\pgfmathsetmacro{\Uy}{abs(\Bx)/sqrt(\Bx*\Bx + \By*\By)}
\pgfmathsetmacro{\Uz}{0}

% Set the vector in the direction of movement, w
\pgfmathsetmacro{\signW}{(\Bx*\Uy-\By*\Ux)/abs(\Bx*\Uy-\By*\Ux)}
\pgfmathsetmacro{\Wx}{\signW*(-\Bz*\Uy)}
\pgfmathsetmacro{\Wy}{\signW*(\Bz*\Ux)}
\pgfmathsetmacro{\Wz}{\signW*(\Bx*\Uy-\By*\Ux)}
\pgfmathsetmacro{\Wnorm}{sqrt(\Wx*\Wx + \Wy*\Wy + \Wz*\Wz)}
\pgfmathsetmacro{\Wx}{\Wx/\Wnorm}
\pgfmathsetmacro{\Wy}{\Wy/\Wnorm}
\pgfmathsetmacro{\Wz}{\Wz/\Wnorm}

% Find the position, velocity, and acceleration in uw-space
\pgfmathsetmacro{\uo}{\Ux*\xo + \Uy*\yo + \Uz*\zo}
\pgfmathsetmacro{\vuo}{\Ux*\vxo + \Uy*\vyo + \Uz*\vzo}
\pgfmathsetmacro{\au}{\Ux*\ax + \Uy*\ay + \Uz*\az}
\pgfmathsetmacro{\wo}{\Wx*\xo + \Wy*\yo + \Wz*\zo}
\pgfmathsetmacro{\vwo}{\Wx*\vxo + \Wy*\vyo + \Wz*\vzo}
\pgfmathsetmacro{\aw}{\Wx*\ax + \Wy*\ay + \Wz*\az}
\pgfmathsetmacro{\gw}{\Wz*\g}

% Set the slope and intercept of the plane's intersection with the front of the strike zone
\pgfmathsetmacro{\slope}{-\Bx/\Bz}
\pgfmathsetmacro{\intercept}{\zo + (\Bx/\Bz)*\xo + (\By/\Bz)*(\yo - (17/12))}

% Find the points of intersection with the ground and 5 feet vertically at the front of the strike zone
\pgfmathsetmacro{\topzone}{(5 - \intercept)/\slope}
\pgfmathsetmacro{\bottomzone}{-\intercept/\slope}

% Find the position of the plane at 55 feet
\pgfmathsetmacro{\toprelease}{\xo + (\By/\Bx)*(\yo - 55) + (\Bz/\Bx)*(\zo-5)}
\pgfmathsetmacro{\bottomrelease}{\xo + (\By/\Bx)*(\yo - 55) + (\Bz/\Bx)*\zo}

% Find the scaled location of the top/back of the plane
\pgfmathsetmacro{\xdistTB}{\toprelease}
\pgfmathsetmacro{\ydistTB}{55 + (73/12)}
\pgfmathsetmacro{\zdistTB}{5 - 2.5}
\pgfmathsetmacro{\radTB}{sqrt(\xdistTB*\xdistTB + \ydistTB*\ydistTB + \zdistTB*\zdistTB)}
\pgfmathsetmacro{\thetaTB}{atan2(\ydistTB,\xdistTB)}
\pgfmathsetmacro{\phiTB}{acos(\zdistTB/\radTB)}
\pgfmathsetmacro{\radscaleTB}{7.5/(sin(\thetaTB)*sin(\phiTB))}
\pgfmathsetmacro{\xTB}{\radscaleTB*cos(\thetaTB)*sin(\phiTB)}
\pgfmathsetmacro{\zTB}{\radscaleTB*cos(\phiTB) + 2.5}

% Find the scaled location of the bottom/back of the plane
\pgfmathsetmacro{\xdistBB}{\bottomrelease}
\pgfmathsetmacro{\ydistBB}{55 + (73/12)}
\pgfmathsetmacro{\zdistBB}{0 - 2.5}
\pgfmathsetmacro{\radBB}{sqrt(\xdistBB*\xdistBB + \ydistBB*\ydistBB + \zdistBB*\zdistBB)}
\pgfmathsetmacro{\thetaBB}{atan2(\ydistBB,\xdistBB)}
\pgfmathsetmacro{\phiBB}{acos(\zdistBB/\radBB)}
\pgfmathsetmacro{\radscaleBB}{7.5/(sin(\thetaBB)*sin(\phiBB))}
\pgfmathsetmacro{\xBB}{\radscaleBB*cos(\thetaBB)*sin(\phiBB)}
\pgfmathsetmacro{\zBB}{\radscaleBB*cos(\phiBB) + 2.5}

% Set the time to the plate
\pgfmathsetmacro{\r}{\vyo/\ay}
\pgfmathsetmacro{\s}{2*(\yo-(17/12))/\ay}
\pgfmathsetmacro{\tplate}{-\r - sqrt(\r*\r - \s)}

% Set time of release
\pgfmathsetmacro{\u}{2*(\yo-55)/\ay}
\pgfmathsetmacro{\trel}{-\r - sqrt(\r*\r - \u)}

% Set time from release to plate
\pgfmathsetmacro{\t}{\tplate - \trel}

% Set the end velocities
\pgfmathsetmacro{\vxend}{\vxo + \tplate*\ax}
\pgfmathsetmacro{\vyend}{\vyo + \tplate*\ay}
\pgfmathsetmacro{\vzend}{\vzo + \tplate*\az}

% Set the number of frames
\pgfmathtruncatemacro{\frames}{int(round(\t*60)+1)}

% Set the time increment
\pgfmathsetmacro{\dt}{\t/(\frames-1)}

% Create the animation
\begin{center}
    \begin{animateinline}[poster=first,loop,controls]{60}
        \whiledo{\them < \frames}{
            \begin{tikzpicture}
                % Clip off anything out of frame
                \clip (-3,0) rectangle (3,5);
                % Sky
                \shade[top color = blue!75!white, bottom color = blue!25!white] (-3,5) -- (3,5) -- (3,2.5) -- (-3,2.5) -- cycle;
                % Grass
                \shade[top color = green!50!black, bottom color = green!70!black] (-3,0) -- (3,0) -- (3,2.447) to [out=179, in =0] (0,2.454) to [out=180, in=1] (-3,2.447) -- (-3,0);
                % Batter's Eye
                \shade[top color = green!60!black, bottom color = green!30!black] (-0.541,3.176) -- (0.541,3.176) -- (0.541,2.5) -- (-0.541,2.5) -- cycle;
                % Bleachers
                \draw[fill = black!85!white] (-3,3.274) to [out=-1, in=180] (-0.541,3.176) -- (-0.541,2.5) -- (-3,2.5) -- cycle;
                \draw[fill = black!85!white] (3,3.274) to [out=181, in=0] (0.541,3.176) -- (0.541,2.5) -- (3,2.5) -- cycle;
                % Outfield Wall
                \shade[top color = green!40!black, bottom color = green!20!black] (-3,2.447) -- (-3,2.659) to [out=-1, in=180] (0,2.639) to [out=0, in=181] (3,2.659) -- (3,2.447) to [out=179, in =0] (0,2.454) to [out=180, in=1] (-3,2.447);
                % Yellow Line
                \draw[yellow] (-3,2.659) to [out=-1, in=180] (0,2.639) to [out=0, in=181] (3,2.659);
                % Mound
                \shade[top color = brown!90!black, bottom color = brown!70!black] (-1.014,2.218) to [out=10, in=180] (0,2.312) to [out=0, in=170] (1.014,2.218) to [out=185, in=0] (0,2.174) to [out = 180, in=355] (-1.014,2.218);
                % Pitching Rubber
                \draw [white] (-0.113,2.312) -- (0.113,2.312);
                         % Plot the pitch plane
                \draw[yellow!80!white] (\topzone,5) -- (\bottomzone,0) -- (\xBB,\zBB) -- (\xTB,\zTB) -- cycle;
                \fill[yellow!80!white, opacity=0.5] (\topzone,5) -- (\bottomzone,0) -- (\xBB,\zBB) -- (\xTB,\zTB) -- cycle;
                \draw[yellow, fill=yellow] (\topzone,5) circle [radius=0.04];
                \draw[yellow, fill=yellow] (\bottomzone,0) circle [radius=0.04];
                \draw[yellow, fill=yellow] (\xBB,\zBB) circle [radius=0.02];
                \draw[yellow, fill=yellow] (\xTB,\zTB) circle [radius=0.02];
                % Time increment between pitches
                \pgfmathsetmacro{\tinc}{\dt*\them + \trel};
                % Current flight time of the pitch
                \pgfmathsetmacro{\time}{\dt*\them};
                % Location of the pitch at the given time
                \pgfmathsetmacro{\xraw}{0.5*\ax*\tinc*\tinc + \vxo*\tinc + \xo};
                \pgfmathsetmacro{\yraw}{0.5*\ay*\tinc*\tinc + \vyo*\tinc + \yo};
                \pgfmathsetmacro{\zraw}{0.5*\az*\tinc*\tinc + \vzo*\tinc + \zo};
                % Velocity of the pitch at the given time
                \pgfmathsetmacro{\vx}{\ax*\tinc + \vxo};
                \pgfmathsetmacro{\vy}{\ay*\tinc + \vyo};
                \pgfmathsetmacro{\vz}{\az*\tinc + \vzo};
                \pgfmathsetmacro{\vel}{sqrt((15*\vx/22)*(15*\vx/22) + (15*\vy/22)*(15*\vy/22) + (15*\vz/22)*(15*\vz/22))};
                % Projection of the in-plane pitch excluding drag
                \pgfmathsetmacro{\uraw}{0.5*\au*\tinc*\tinc + \vuo*\tinc + \uo};
                \pgfmathsetmacro{\wraw}{0.5*\aw*\tinc*\tinc + \vwo*\tinc + \wo};
                \pgfmathsetmacro{\vu}{\au*\tinc + \vuo};
                \pgfmathsetmacro{\vw}{\aw*\tinc + \vwo};
                \pgfmathsetmacro{\uproj}{0.5*\au*(\tplate - \tinc)*(\tplate - \tinc) + \vu*(\tplate - \tinc) + \uraw};
                \pgfmathsetmacro{\wproj}{0.5*\gw*(\tplate - \tinc)*(\tplate - \tinc) + \vw*(\tplate - \tinc) + \wraw};
                \pgfmathsetmacro{\xplane}{\Ux*\uproj + \Wx*\wproj + \Bx*\Bfixed};
                \pgfmathsetmacro{\zplane}{\Uz*\uproj + \Wz*\wproj + \Bz*\Bfixed};
                % Calculate the drag
                \pgfmathsetmacro{\vxbar}{(\vx+\vxend)/2};
                \pgfmathsetmacro{\vybar}{(\vy+\vyend)/2};
                \pgfmathsetmacro{\vzbar}{(\vz+\vzend)/2};
                \pgfmathsetmacro{\vbar}{1.25*sqrt((\vxbar/1.25)*(\vxbar/1.25) + (\vybar/1.25)*(\vybar/1.25) + (\vzbar/1.25)*(\vzbar/1.25))};
                \pgfmathsetmacro{\vcoeff}{-abs(\ax*(\vxbar/\vbar) + \ay*(\vybar/\vbar) + (\az-\g)*(\vzbar/\vbar))};
                \pgfmathsetmacro{\axdrag}{\vcoeff*(\vxbar/\vbar)};
                \pgfmathsetmacro{\aydrag}{\vcoeff*(\vybar/\vbar)};
                \pgfmathsetmacro{\azdrag}{\g + \vcoeff*(\vzbar/\vbar)};
                % Contribution of drag in the w-direction
                \pgfmathsetmacro{\awdrag}{\Wx*\axdrag + \Wy*\aydrag + \Wz*\azdrag};
                % Projection of the in-plane pitch into the strike zone including drag
                \pgfmathsetmacro{\wprojdrag}{0.5*\awdrag*(\tplate - \tinc)*(\tplate - \tinc) + \vw*(\tplate - \tinc) + \wraw};
                \pgfmathsetmacro{\xplanedrag}{\Ux*\uproj + \Wx*\wprojdrag + \Bx*\Bfixed};
                \pgfmathsetmacro{\zplanedrag}{\Uz*\uproj + \Wz*\wprojdrag + \Bz*\Bfixed};
                % Distance to the catcher's viewpoint
                \pgfmathsetmacro{\xdist}{\xraw};
                \pgfmathsetmacro{\ydist}{\yraw + (73/12)};
                \pgfmathsetmacro{\zdist}{\zraw - 2.5};
                % Spherical coordinates of the pitch
                \pgfmathsetmacro{\rad}{sqrt(\xdist*\xdist + \ydist*\ydist + \zdist*\zdist)};
                \pgfmathsetmacro{\theta}{atan2(\ydist,\xdist)};
                \pgfmathsetmacro{\phi}{acos(\zdist/\rad)};
                \pgfmathsetmacro{\radscale}{7.5/(sin(\theta)*sin(\phi))};
                % Location of the pitch from the catcher's perspective
                \pgfmathsetmacro{\xscale}{\radscale*cos(\theta)*sin(\phi)};
                \pgfmathsetmacro{\zscale}{\radscale*cos(\phi) + 2.5};
                \pgfmathsetmacro{\rscale}{(7.5*0.125)/\rad};
                % Plot the pitch
                \draw[shading = ball, ball color = white] (\xscale,\zscale) circle [radius=\rscale];
                % Plot the strike zone
                \draw[black!85!white] (-17/24,1.5) -- (17/24,1.5) -- (17/24,3.5) -- (-17/24,3.5) -- cycle;
                % Plot both projections
                \draw[red!80!white] (\xplane,\zplane) circle [radius=0.125];
                \draw[blue!80!white,dashed] (\xplanedrag,\zplanedrag) circle [radius=0.125];
                % Display the metrics
                \node[above right] at (-3,4.4) {Dist.: };
                \node[above left] at (-1,4.4) {\pgfmathprintnumber[precision=1,fixed]{\yraw}};
                \node[above right] at (-1.2,4.4) {ft};
                \node[above right] at (0,4.4) {Vel.: };
                \node[above left] at (2.1,4.4) {\pgfmathprintnumber[precision=1,fixed]{\vel}};
                \node[above left] at (3,4.325) {mph};
                \node[above right] at (-3,0) {Time: };
                \node[above left] at (-0.9,0) {\pgfmathprintnumber[precision=2,fixed]{\time}};
                \node[above right] at (-1.1,0) {sec};
            \end{tikzpicture}
            \stepcounter{m}
            \ifthenelse{\them < \frames}{
                \newframe
            }
            {
                \end{animateinline} \relax
            }
        }
\end{center}

\end{document}